Got it. Appreciate the feedback. What if I have neutral? Do I pass that through the transformer? How does it know to find the center tap to properly give you 120 between phases?
My example was based on a single phase 208V line to neutral source. And a single boost transformer.
If you bring in all three (or two out of three) phases boost function gets more complicated.
If you start with a 208Y/120 source, the easiest boost configuration to understand is to use three 120 to 139 volt boost transformers to get a 240Y/139 source with the same central point as the neutral.
If you use a boost transformer connected line to line to get the 208V input, you will get a 240V output where one end still has 120V to the neutral and the other does not. (I have not done the vector analysis to see just what that voltage is.
If you start with a 208V delta, with no neutral or ignoring the neutral, you could use two boost transformers to get an assymmetric open delta 240 or you can use three boost transformers to get a symmetric closed delta 240V in which no output leads is common with an input lead.
You cannot use a boost transformer on a 208V wye to get a 120-0-120 source with a neutral. You will have to use an isolation transformer so that you can ground the center tap of the output. And that transfomer will need to be fully rated for the load.